Experimental and theoretical studies on induced ferromagnetism of new (1 − x)Na0.5Bi0.5TiO3 + xBaFeO3−δ solid solution

New solid solution of Na0.5Bi0.5TiO3 with BaFeO3−δ materials were fabricated by sol–gel method. Analysis of X-ray diffraction patterns indicated that BaFeO3−δ materials existed as a well solid solution and resulted in distortion the structure of host Na0.5Bi0.5TiO3 materials. The randomly incorporated Fe and Ba cations in the host Na0.5Bi0.5TiO3 crystal decreased the optical band gap from 3.11 to 2.48 eV, and induced the room-temperature ferromagnetism. Our density-functional theory calculations further suggested that both Ba for Bi/Na-site and Fe dopant, regardless of the substitutional sites, in Na0.5Bi0.5TiO3 lead to the induced magnetism, which is illustrated in terms of the exchange splitting between spin subbands through the crystal field theory and Jahn–Teller distortion effects. Our work proposes a simple method for fabricating lead-free ferroelectric materials with ferromagnetism property for multifunctional applications in smart electronic devices.

. In the periodic table of elements, Ba is the largest radius in alkaline earth metals, thus, we expected that the co-modification of Ba cations at A-site and Fe cations at B-site, respectively, of host Na 0.5 Bi 0.5 TiO 3 materials were resulted exhibition large magnetization during solid solution of BaFeO 3−δ into Na 0.5 Bi 0.5 TiO 3 materials.
In this work, new system (1-x)Na 0.5 Bi 0.5 TiO 3 + xBaFeO 3−δ materials as solid solution were fabricated by sol-gel method. The BaFeO 3−δ materials were well solid solution into the host Na 0.5 Bi 0.5 TiO 3 materials through diffusion and random incorporation of Ba and Fe cations with host lattice of Na 0.5 Bi 0.5 TiO 3 materials. The structural distortion and reduced optical band gap of host Na 0.5 Bi 0.5 TiO 3 materials were obtained. The complex magnetic properties of BaFeO 3−δ -modified Na 0.5 Bi 0.5 TiO 3 materials was obtained as function of BaFeO 3−δ amounts addition. Figure 1a,b shows the EDS spectral of pure Na 0.5 Bi 0.5 TiO 3 samples and BaFeO 3−δ -modified Na 0.5 Bi 0.5 TiO 3 sample with 5 mol.% BaFeO 3−δ , respectively. The inset of each figure showed the selected area for EDS elements characterization. All expectational elements such Bi, Na, Ti and O were obtained in EDS spectral of pure Na 0.5 Bi 0.5 TiO 3 samples, as shown in Fig. 1a. The addition of the Ba and Fe peaks were showed in the EDS spectral of BaFeO 3−δ -modified Bi 0.5 Na 0.5 TiO 3 samples, as expected, which were presented at the Fig. 1b. The results provided that the BaFeO 3−δ impurities existed in our samples.

Results and discussion
The chemical maps of Bi 0.5 Na 0.5 TiO 3 materials modified with 9 mol.% BaFeO 3−δ were analyzed. The distribution of impurity elements in the Na 0.5 Bi 0.5 TiO 3 materials modified with 9 mol.% BaFeO 3−δ is shown in Fig. 2. The surface morphology of the area selected for chemical mapping is shown in Fig. 2a www.nature.com/scientificreports/ Ba, and Fe elements are shown in Fig. 2c-h, respectively. The results clearly demonstrated that the constituent chemical elements were homogenously dispersed in the sample. Figure 3 (a) shows the X-ray diffraction patterns of pure Na 0.5 Bi 0.5 TiO 3 and BaFeO 3−δ -modified Na 0.5 Bi 0.5 TiO 3 with various BaFeO 3−δ concentrations. On the basis of diffraction peak position and relative to intensity, all samples were indexed to a perovskite structure with the rhombohedral symmetry of the Na 0.5 Bi 0.5 TiO 3 compound (JCPDS card no. 00-036-0340, space group R3c). In addition, the impurities phase or phase segregation was not founded in the X-ray diffraction patterns. All X-ray diffraction pattern of BaFeO 3−δ -modified Na 0.5 Bi 0.5 TiO 3 samples were indexed to follow the structural of Na 0.5 Bi 0.5 TiO 3 compound. The results indicated that BaFeO 3−δ materials exhibited a well solid solution in Na 0.5 Bi 0.5 TiO 3 materials. In other word, the Ba and Fe cations were diffused to randomly incorporate with host lattice of Na 0.5 Bi 0.5 TiO 3 compound as solid solution. In order to    Fig. 3b. The setline peaks were overloaded together which were distinguished via Lorentz fitting, as shown in dot line of Fig. 3b. The results clearly indicated that the diffraction peaks of Na 0.5 Bi 0.5 TiO 3 materials trended to shift to lower diffraction angle as increasing the BaFeO 3−δ amounts, which provided the evident for expansion of lattice parameter. Furthermore, the lattice parameters a and c of the pure Bi 0.5 Na 0.5 TiO 3 and the BaFeO 3-δ -modified Bi 0.5 Na 0.5 TiO 3 as a function of BaFeO 3-δ addition amounts are shown in Fig. 3c. The results show that the distorted lattice parameters of the Bi 0.5 Na 0.5 TiO 3 compound are not a linear function of the concentrations of the BaFeO 3-δ solid solution, which showed complex lattice parameter distortion. This result could be attributed to the different radii of Ba and Fe cations in the additives and that of Bi, Na, and Ti incorporated randomly in the lattice of the host Na 0.5 Bi 0.5 TiO 3 materials. Based on the Shamon' reported, the radius of Ba 2+ and Fe 2+/3+ cations were 1.61 Å and 0.645 Å/0.780 Å, respectively, while the radius of Bi 3+ , Na + and Ti 4+ cations were 1.17 Å, 1.39 Å and 0.605 Å, respectively 51 . Therefore, the Fe cations diffused to substitute for Ti-sites in perovskite structural of Na 0.5 Bi 0.5 TiO 3 crystal, resulted in expansion of the lattice. The fact that the radius of Ba 2+ cations are larger than that of both Bi 3+ and Na + cations were also reflected by expanding the lattice parameter of host Na 0.5 Bi 0.5 TiO 3 compound. However, we noted that the oxygen vacancies were generated due to unbalance of valence states of Fe 2+/3+ and Ti 4+ at B-site and Ba 2+ for Bi 3+ at A-site. In addition, the Na vacancies were created when Ba 2+ substitute Na + . The oxygen vacancies (¤) has radius of 1.31 Å which were smaller than that of oxygen anion (O 2-) of 1.4 Å 52 . Therefore, the existence of oxygen vacancies in the structure led to reduction of the lattice parameter. The structural distortion of Na 0.5 Bi 0.5 TiO 3 materials was due to co-modification at A-and B-site via alkali earth and transition metal, respectively, which was consistent with recently reported [28][29][30] .
In other word, the X-ray diffraction characterization of BaFeO 3−δ -modified Na 0.5 Bi 0.5 TiO 3 samples provided that the BaFeO 3−δ materials were well solid solution into host Na 0.5 Bi 0.5 TiO 3 materials. Figure 4a show the Raman scattering of pure Na 0.5 Bi 0.5 TiO 3 materials and BaFeO 3−δ -modified Na 0.5 Bi 0.5 TiO 3 materials with various of BaFeO 3−−δ concentration as solid solutions at room temperature. The results provide that the shape of Raman scattering spectra seem to be unchanged in comparison between that of pure Na 0.5 Bi 0.5 TiO 3 materials and that of BaFeO 3−δ -modified Na 0.5 Bi 0.5 TiO 3 s materials. In the wave number ranging from 300 cm −1 to 1000 cm −1 , the Raman spectra were possible divided into three main regions and they overlapped each other. The three main band regions were in the range of 300-450 cm −1 , 450-700 cm −1 and 700-1000 cm −1 , respectively. The combination of experimental investigation and first principles density functional theoretical calculation for Raman vibration modes of Na 0.5 Bi 0.5 TiO 3 materials exhibited that the lowest frequency modes in range of  Fig. 4b) trended to shift to high frequency, which were suggested to be related to distorted structure of (Ti,Fe)O 6 framework and/or effective mass effect because of difference between the radius and mass of impurities Fe and host Ti at B-site [28][29][30] . In other word, the shifted Raman scattering modes confirmed the substitution of Ba and Fe into the host lattice of Na 0.5 Bi 0.5 TiO 3 materials. Figure 5a shows the optical absorption spectra of pure Na 0.5 Bi 0.5 TiO 3 and BaFeO 3−δ -modified Na 0.5 Bi 0.5 TiO 3 with various BaFeO 3−δ concentrations. Pure Na 0.5 Bi 0.5 TiO 3 samples exhibited a single absorbance edge, consistent with the reported optical properties of Na 0.5 Bi 0.5 TiO 3 materials [9][10][11]55 . However, pure Na 0.5 Bi 0.5 TiO 3 materials exhibited the unsharp transition which were tailored with slightly tail. The small tail at long wavelength in absorbance spectroscopy of pure Na 0.5 Bi 0.5 TiO 3 materials were suggested to be related with self-defect and/or surface effect cause of unsaturation bonding pair of atoms at the surface 55,56 . The addition BaFeO 3−δ to Na 0.5 Bi 0.5 TiO 3 material as solid solution led to a red shift of the absorbance edge. The appearance of peaks around 485 nm in  Oxygen vacancies created because of unbalanced charges between impurities and hosts (e.g. Fe 2+/3+ substitute for Ti 4+ , and Ba 2+ replacement for Bi 3+ ) also led to the reduction in the optical band gap because the oxygen vacancy states normally located below and near the conduction band 9-11,59,60 . Thus, we suggest that the random substitution of Ba and Fe ions into the host Na 0.5 Bi 0.5 TiO 3 could alter the electronic band structure, resulting in reduction of the optical band gap. Figure 6a shows the room-temperature PL emission spectra of pure Na 0.5 Bi 0.5 TiO 3 and BaFeO 3−δ -modified Na 0.5 Bi 0.5 TiO 3 samples with various BaFeO 3−δ amount. The PL spectral of all samples exhibited a broad band emission while strong emission showed in range from 479 to 505 nm. The addition of BaFeO 3−δ into host Na 0.5 Bi 0.5 TiO 3 materials as solid solution suppressed the emission peak, as shown in inset of Fig. 6a. However, we noted that a slight addition of BaFeO 3−δ concentration enhanced the emission intensity. In addition, the PL spectral of pure Na 0.5 Bi 0.5 TiO 3 and BaFeO 3−δ -modified Na 0.5 Bi 0.5 TiO 3 samples was overlapped together, suggesting to multi-emission peaks with closed together. Thus, we tried to distinguish the multi-emission peaks via Lorentz fitting. The deconvoluted emission peaks of pure Na 0.5 Bi 0.5 TiO 3 samples were shown in Fig. 6b. The broad band visible luminescence was also recently reported for ferroelectric titanates-based materials at room temperature such as BaTiO 3 , SrTiO 3 , PbTiO 3 etc. 61 . The observations in broad band emission were also archived in Bi 0.5 K 0.5 TiO 3 materials, which were related to the surface effect and/or self-defect effect 56 . Normally, the coordination status of the atoms at the surface of materials is unsaturated, resulting in unpaired states, that make them different from that in the bulk 62 . The unsaturated atoms that existed at the surface region of Na 0.5 Bi 0.5 TiO 3 materials formed local levels in the forbidden gaps, this displayed the effect of the self-trapped excitons 63 . Therefore, the incident photon was absorbed by the Na 0.5 Bi 0.5 TiO 3 powder as it is illuminated with the excited source. The absorption photons could create some localized levels and form small polarons. The interaction between the holes in the valence band and polarons formed by the intermediate self-trapped excitons caused blue shift of the luminescence 63 . In addition, the structural distortion because of coupling of TiO 6 -TiO 6 adjacent octahedra generate the localized electronic levels above the valence band. The recombination from these levels may result in the photoluminescence of Bi 0.5 K 0.5 TiO 3 materials 62 . The photoluminescence of ferroelectric materials is not generally governed by band-to-band transition, owning to the difficulty in recombination of electron-hole pairs and the separation of the natural polarization domain in the materials. In this kind of materials, the surface states were in charge of the luminescence, in which many unsaturated atoms that presented on the surface of the ferroelectric materials creates the localized levels in the forbidden gaps. Interestingly, the intensity of PL emission of Na 0.5 Bi 0.5 TiO 3 materials was suppressed by the addition of BaFeO 3−δ , as shown in the inset of Fig. 6b. The PL emission spectra of BaFeO 3−δ -modified Na 0.5 Bi 0.5 TiO 3 materials did not change, indicating the lack of Ba and Fe substitution at the A-and B-sites, respectively, in the new electron-hole transitions. Thus, the substitution of Fe cation with Ti at the octahedral sites created oxygen vacancies; such vacancies acted as the chapping electron www.nature.com/scientificreports/ generated from absorbance photon energy, thereby prevented the recombination of the electron-hole pairs to generate photons. Furthermore, the role of BaFeO 3−δ solid solution in Na 0.5 Bi 0.5 TiO 3 materials in imparting magnetism was dependent on the applied magnetic field at room temperature, as shown in Fig. 7a-g for pure Na 0.5 Bi 0.5 TiO 3 and BaFeO 3−δ -modified Na 0.5 Bi 0.5 TiO 3 materials with BaFeO 3−δ concentration of 0.5, 1, 3, 5, 7 and 9 mol%, respectively. The pure Na 0.5 Bi 0.5 TiO 3 exhibited the anti-S-shape in M-H curves, indicating the combination of diamagnetism and weak ferromagnetism, as shown in Fig. 7a. The diamagnetism in pure Na 0.5 Bi 0.5 TiO 3 samples originated from the electronic configuration of Ti 4+ as 3d°, whereas the weak ferromagnetism originated from self-def ects [9][10][11]14,16,30,64,65 . The typical hysteresis loop of ferromagnetism was obtained for pure Na 0.5 Bi 0.5 TiO 3 materials after subtract the diamagnetic components, as shown in inset of Fig. 7a. The saturation magnetization was estimated around 1.5 memu/g which were well consisted with recently reported by Ju et al. 16 . In addition, the remanent magnetization (M r ) and coercive field (H C ) of pure Na 0.5 Bi 0.5 TiO 3 materials were approximately 0.11 memu/g and 73 Oe, respectively, which were solid evidence for presentation of ferromagnetic state at room temperature. The estimation for their values were also performed with recently reported by Thanh et al. and Ju et al. which those were possibly originated from self-defect such as Na-, Ti-or O-vacancies 10,16 . The M-H curves trend to switch from anti-S-shape to S-shape in the BaFeO 3−δ -modified Na 0.5 Bi 0.5 TiO 3 samples as the BaFeO 3−δ concentration in the solid solution increase, providing evidence regarding the strength enhancement of ferromagnetic ordering in the samples. As shown in Fig. 7c, the typical ferromagnetic hysteresis loops were obtained where the magnetization trended to saturate as the external applied magnetic field increase, and the strength of ferromagnetic increase. However, further increasing amounts of BaFeO 3−δ into host Na 0.5 Bi 0.5 TiO 3 , the M-H curves exhibited the unsaturation with low applied external magnetic field, as shown in Fig. 7d-g. The dependence of shape in magnetic hysteresis loop of BaFeO 3−δ -modified Na 0.5 Bi 0.5 TiO 3 materials represented that the magnetic properties of BaFeO 3−δ -modified Na 0.5 Bi 0.5 TiO 3 materials were very complex, on the one hand the magnetic properties of Na 0.5 Bi 0.5 TiO 3 materials were strong dependent of the concentration of BaFeO 3−δ as solid solution. The M r and H C values of BaFeO 3−δ -modified Bi 0.5 Na 0.5 TiO 3 materials were approximately 51-106 Oe and 0.12-0.48 memu/g, respectively. These results were consistent with the recently observed M r and H C of transition-metal-doped lead-free and lead-based ferroelectric materials [8][9][10][11]60,[64][65][66][67][68] . The nonzero M r and H C values of BaFeO 3−δ -modified Bi 0.5 Na 0.5 TiO 3 materials provided solid evidence for the presence of the ferromagnetic state at room temperature. In additon, the maximum magnetization was estimated around 23 memu/g for 9 mol% BaFeO 3−δ solid solution in host Na 0.5 Bi 0.5 TiO 3 materials. That value was larger than that of self-defect induced magnetism of pure Na 0.5 Bi 0.5 TiO 3 materials or single transition metals doped Na 0.5 Bi 0.5 TiO 3 materials, in which around ~ 1.5 memu/g for Cr-doped Na 0.5 Bi 0.5 TiO 3 , ~ 3 memu/g for Co-doped Na 0.5 Bi 0.5 TiO 3 , ~ 9 memu/g for Mn-doped Na 0.5 Bi 0.5 TiO 3 , ~ 15 memu/g for Fe-doped Na 0.5 Bi 0.5 TiO 3 materials, and ~ 4 memu/g for Ni-doped Na 0.5 Bi 0.5 TiO 3 materials [8][9][10][11]60,68 . Herein, we need to remark that the origin of ferromagnetism ordering of transition metal impurities containing Na 0.5 Bi 0.5 TiO 3 materials at room temperature were still debated. The weakferromagnetism in pure Na 0.5 Bi 0.5 TiO 3 materials were possibly originated from self-defect and/or surface defect (such as Ti and Na-vacancies) while the magnetization of Na 0.5 Bi 0.5 TiO 3 materials were slightly enhanced via oxygen vacancies 11,14,16,30 . The Mn-, Ni-and Fe-doped Na 0.5 Bi 0.5 TiO 3 materials exhibited the room temperature ferromagnetism which were related to intrinsic phenomenon where the transition cations such of Mn, Ni and Fe interacted with the oxygen vacancies, like F-center interaction mechanism, e.g. Mn 2+/3+ -¤-Mn 2+/3+ or Fe 2+/3+ -¤-Fe 2+/3+ pairs etc., which were favored for ferromagnetic ordering 8-11,60,64 . Unlikely Mn-, Ni-and www.nature.com/scientificreports/ Fe-cations impurities in Na 0.5 Bi 0.5 TiO 3 materials, the Co impurities trended to form Co-clusters embedding in host Na 0.5 Bi 0.5 TiO 3 materials which displayed the room temperature ferromagnetism 8 . Recently, our experimental observation along with first principle calculation predicted that the interaction of Co cations into host Na 0.5 Bi 0.5 TiO 3 materials possibly displayed the weak ferromagnetism at room temperature 64 . In addition, Hung et al. reported that MgFeO 3−δ solid solution in Na 0.5 Bi 0.5 TiO 3 materials exhibited strong magnetization, which were estimated to be around 39.6 memu/g, where the Mg cations played an importance role for mediating ferromagnetism 28 . The SrFeO 3−δ -andCaFeO 3−δ -modified Na 0.5 Bi 0.5 TiO 3 materials also showed strong enhancement of the magnetization at room temperature 29,30 . Note that the Mg cations possibly substituted for both A-site (Bi 3+ , Na + ) and B-site in Na 0.5 Bi 0.5 TiO 3 crystal structure while Sr and Ca cations only replaced with A-site in host Na 0.5 Bi 0.5 TiO 3 crystal structure [28][29][30] . Thus, we suggested that the possible room temperature ferromagnetism in BaFeO 3−δ -modified Na 0.5 Bi 0.5 TiO 3 materials were strongly related to the interaction of Fe cations through oxygen vacancies, like F-central interaction, which were recently suggested for Mn-, Ni-, Co-and Fe-doped Na 0.5 Bi 0.5 TiO 3 materials 9,10,60,64,69 . A recent X-ray photoelectron spectroscopy (XPS) analysis of CaFeO 3−δ -modified Na 0.5 Bi 0.5 TiO 3 materials showed that Fe cations are stable in the Fe 2+ and Fe 3+ valence state together with O vacancies 30 . Therefore, we suggest that the interaction pair Fe 2+/3+ -¤-Fe 2+/3+ favors ferromagnetic ordering 69  In addition, isolated Fe cations displayed paramagnetic properties 9,69-73 . Thus, the combination of the complex signal of ferromagnetic interaction and antiferromagnetic-like and paramagnetic properties was observed when the BaFeO 3−δ solid solution was present at high concentrations in host Na 0.5 Bi 0.5 TiO 3 materials. However, unlike single Fe-doped Na 0.5 Bi 0.5 TiO 3 materials, the modification at A-site (Bi 3+ , Na + ) via Ba 2+ cations in host Na 0.5 Bi 0.5 TiO 3 materials also possibly contributed a source to the ferromagnetism ordering, in which the substitution of Ba 2+ cations for Bi 3+ cations in crystal structure created the O-vacancies while Ba 2+ cations incorporated for Na + cations generated the Na-vacancies. Both O-and Na-vacancies are origin of the ferromagnetism, but they work in different ways 16,30 . Nevertheless, both the experimental observation and theoretical prediction have agreed that Na-vacancies induce the nonzero magnetic moment 16,30 . Therefore, the strength of magnetic moments can be increased by increasing the number of Na-vacancies. However, unlikely Na-vacancies, the O-vacancies were predicted to be agent of the nonmagnetic moment 30 84 . Therefore, we suggested that Fe cations were random incorporated at both the A-site and B-site likely contributing to the complex magnetic properties of the host Bi 0.5 Na 0.5 TiO 3 materials. The role of Fe cation substitution at the A-and B-sites in the magnetic properties of Na 0.5 Bi 0.5 TiO 3 materials was further investigated by using density-functional theory (DFT) calculation.
To elucidate the origin of the observed ferromagnetism in BaFeO 3−δ -doped Na 0.5 Bi 0.5 TiO 3 , the density-functional theory (DFT) calculations were performed using the Vienna ab initio Simulation Package (VASP) 85,86 . The generalized gradient approximation (GGA) formulated by Perdew, Burke, and Ernzerhof (PBE) was used for the electron exchange correlation potential 87 . Figure 8a shows the side and top views of the rhombohedral crystal structure of the 24 formula unit (f.u.) cell (120-atom) adopted for Bi 0.5 Na 0.5 TiO 3 (BNT). As model systems shown in Fig. 8b,c,  www.nature.com/scientificreports/ zone integration. To obtain optimized atomic structures, the atomic positions as well as lattice parameters were fully relaxed until the largest force becomes less than 10 −2 eV/Å and the change in the total energy between two ionic relaxation steps is smaller than 10 −5 eV. Note that the severe distortions of octahedral TiO 3 lattice were observed for all geometries after optimization. We first investigate the energetics of the Ba-and Fe-doped BNT. Here, the formation energy (H f ) is defined as  Table 1. We find that the H f of BNT is -2.385 eV/atom, which indicates the pure BNT is quite stable. Our calculations further indicate that the Ba substitute prefers either the Bi or Na sites (A-site), as their enthalpies of formation are competitive (− 2.402 and − 2.392 eV/atom). The Fe dopant atoms may also occupy both the A-and B-site (Ti), although the absolute values of H f for the A-site (− 2.376 eV/atom for the Bi and − 2.355 eV/atom for the Na) are higher than that (− 2.335 eV/atom) of the B (Ti)-site in magnitude. Nevertheless, in a real sample, the latter substitution (B-site) might appear more than the A-site (Bi and Na) substitution, as the A-site is mainly occupied by the Ba atoms. Table 1 shows the calculated magnetic energy (ΔE = E sp -E non-sp , where E sp and E non-sp are the total energies of the spin-polarized and non-spin-polarized states, respectively), total magnetization per f.u. (M), and atom   Table 1. In particular, for BNT(Fe), a finite DOS peak state appears right at the Fermi level in the majority-spin state while the other spin channel exhibits an insulating behavior. This is a feature of the half-metallic electronic nature. Furthermore, for all the Fe-doped compounds, substantially large exchange splitting between the spin subbands (i.e., majority-spin and minority-spin) is prominent (Fig. 10). These peak states are due to the strong orbital hybridization between the Fe 3d and O 2p states. As shown in Fig. 11, the majority-spin bands of the Fe are fully occupied, and the minority-spin states are almost unoccupied for the BNT(Fe) and B(Fe)NT but partially occupied for the BN(Fe)T. Overall, one can expect the large magnetic moment at the Fe site, as addressed in Table 1. Induced moments at the neighboring sites to the Fe are rather small. Based on the PDOS analyses for the BNT(Fe) and B(Fe)NT compounds, we infer that the six (five) d-orbitals of Fe 2+ (Fe 3+ ) ion split by high-spin state through the crystal field theory are filled by the 5 majority-spin electrons in the low-lying t 2g orbital levels and 1 electrons (no electron) in the minority-spin t 2g state. Thus, according to Hund's rule, the calculated magnetic moments of 4 and 5 μ B of the Fe replacement for the Ti and Bi sites can be explained by the electronic configuration of the high-spin state in the crystal field theory through the unpaired electron spin count. For the BN(Fe)T, the magnetic moment of the Fe atom is reduced compared with those for the other two systems, as some minority-spin states are partially occupied (Fig. 11c). Furthermore, for all compounds, both the t 2g and e g states in PDOS are slightly split, which is mainly due to the Jahn-Teller effect as the severe octahedron distortion occurs in the presence of the Fe substitution.
We now investigate the doping concentration dependent magnetization of the Fe and Ba doped BNT.   www.nature.com/scientificreports/ is much larger than the measured values (23 memu/g at 9 mol.%), which is presumably due to the different concentrations and stoichiometries between the theory (here only the Fe doping) and experiment (Ba and Fe co-doping). Interestingly, the Ba doping for the A-site (Bi and Na) induces magnetism (M = 0.05 µ B /f.u.) at about 2.5 at.% (Fig. 12). It is further found that the calculated magnetization increases as the doping concentration increases. Our atom resolved magnetization analyses indicate that the induced magnetization mainly comes from the Ti and O atoms neighboring to the Ba dopant site. The underlying mechanism can be explained by the spin-polarized charge transfer between the dopant and neighboring atoms in the unit cell, as revealed from the Ti-and O-PDOS analyses shown in Fig. 13. We finally explored the magnetic and electronic properties of the O-vacancy defected BNT(Fe). We have considered the presence of a single vacancy and double vacancies in the Fe-included octahedral cell to imitate different valence states of the Fe dopant atom. Our calculations show that the total magnetization (4 μ B ) of the BNT(Fe) compound decreases by 1 and 2 μ B for the single-vacancy and double-vacancy systems, respectively. From the electronic structure analyses shown in Fig. 14a-c, the PDOS of the Fe dopant atom in BNT(Fe) shift toward the low energy region and some minority-spin states are partially occupied in the presences of the single and double oxygen vacancies. This is because of the extra electrons accumulated at the Fe site, originated from  www.nature.com/scientificreports/ the O deficiency in the unit cell. Furthermore, the obtained magnetic moments are simply the reflections of the Fe 2+ and Fe 3+ ionic states in the high spin states and mixture of them in a real sample, as addressed in the previous experiment 30 .

Conclusion
The solid solution of BaFeO 3−δ and Na 0.5 Bi 0.5 TiO 3 ceramics have been successfully synthesized by a chemical route sol-gel method. The Ba and Fe ions were distributed randomly into the Na 0.5 Bi 0.5 TiO 3 lattices which caused in the distortion of lattice structure and decreased the optical band gap. The complex magnetic properties were observed in this solid solution. This work shows a simple way for enhancement of room-temperature ferromagnetism in lead-free ferroelectric materials by solid solution.

Experiment
(1 − x)Na 0.5 Bi 0.5 TiO 3 + xBaFeO 3−δ (BNT-xBFO; x = 0.5%, 1%, 3%, 5%, 7% and 9%) samples were fabricated by sol-gel method. The raw materials were consisted of Bi(NO 3 ) 3 . 5H 2 O, NaNO 3 , Fe(NO 3 ) 3 . 9H 2 O, tetraisopropoxytitanium (IV) (C 12 H 28 O 4 Ti) and BaCO 3 . The solution was chosen which are acetic acid (CH 3 COOH) and deionized water with volume ratio of V H 2 O :V CH 3 COOH = 5:2 while an acetylacetone (CH 3 COCH 2 COCH 3 ) were selected as ligand. Fist, the BaCO 3 were weighted and distinguee under mix acid acetic and deionized water. Thus, the raw materials such Bi(NO 3 ) 3 .5H 2 O, NaNO 3 , Fe(NO 3 ) 3 .9H 2 O were weighted to add the solution. To following, the solution was added with tetraisopropoxytitanium after adding to avoid hydrolysis. The solution was magnetic stirred under several hours to make homogeneous solution of sol. The sol was dried under 100 °C to prepare gels in oval. The dried gel was rout grounded and annealed under 800 °C for three hours in air then nature cooling down to room temperature. The as-prepared samples were rout ground for further samples characterization.